Abstract
In a vertically oscillating circular cylindrical container, singular perturbation theory of two-time scale expansions was developed in inviscid fluids to investigate the motion of single free surface standing wave including the effect of surface tension. A nonlinear slowly varying amplitude equation, which incorporates cubic nonlinear term, external excitation and the influence of surface tension, was derived from potential flow equation. The results show that, when forced frequency is lower, the effect of surface tension on mode selection of surface wave is not important. However, when forced frequency is higher, the surface tension can not be neglected. This proved that the surface tension causes free surface returning to equilibrium location. In addition, due to considering the effect of surface tension, the theoretical result approaches to experimental results much more than that of no surface tension.
Similar content being viewed by others
References
Zhang W, Viñal J. Pattern formation in weakly damped parametric surface waves[J]. J Fluid Mech, 1997, 336(7):301–330.
Ciliberto S, Gollub J P. Chaotic mode competition in parametrically forced surface waves[J]. J Fluid Mech, 1985, 158(17):381–398.
Kudrolli A, Gollub J P. Pattern and spatiotemporal chaos in parametrically forced surface waves: a systematic survey at large aspect ratio[J]. Physica D, 1996, 97(1):113–154.
Pushkarev A N. Turbulence of capillary waves[J]. Phys Rev Lett, 1996, 76(18):3320–3323.
E Xuequan, Gao Yuxin. Ordered and chaotic modes of surface wave patterns in a vertically oscillating fluid[J]. Communications in Nonlinear Sciences and Numerical Simulation, 1996, 1(2):1–6.
E Xuequan, Gao Yuxin. Visualization of surface wave patterns of a fluid in vertical vibration[C]. In: Wei Qingding (ed). Proceedings of the Fourth Asian Symposium on Visualization. International Academic Publishers, Beijing, 1996, 653–658.
Gao Yuxin, E Xuequan. Surface wave visualization for liquid in micro-amplitude vibration[J]. Experimental Mech, 1998, 13(3):326–333 (in Chinese).
Jian Yongjun, E Xuequan, Bai Wei. Nonlinear Faraday waves in a parametrically excited circular cylindrical container[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(10):1194–1207.
Jian Yongjun, E Xuequan. Surface wave structure in a vertically forced circular cylindrical vessel[J]. J Hydrodynamics, 2003, 18(2):135–147 (in Chinese).
Jian Yongjun. Study on the Nonlinear Surface Waves and Their Instability Analysis in a Circular Cylindrical Container Subjected to Vertical Excitation[D]. Ph D Dissertation. Institute of Mechanics, Chinese Academy of Sciences, Beijing, 2003, 50–61 (in Chinese).
Author information
Authors and Affiliations
Corresponding author
Additional information
Project supported by the National Natural Science Foundation of China (Nos. 19772063 and 19772068) and the Doctoral Research Fund of the Ministry of Education (No.20010141024)
Rights and permissions
About this article
Cite this article
Jian, Yj., Xue-quan, E. & Zhang, J. Capillary effect on vertically excited surface wave in circular cylindrical vessel. Appl Math Mech 27, 227–234 (2006). https://doi.org/10.1007/s10483-006-0211-1
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s10483-006-0211-1